Abstract
In this paper, the new definition of probabilistic norm of linear operators on a PN space is given. In virtue of this, the boundedness of linear operators is described and the completemess of the PN space composed of all bounded linear operators is showed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. Radu. On a random norm and continuity of linear operators on random normed spaces,C. R. Acad. Sci. Paris,280 (1975), 80–89.
Zhang Shisheng, Basic theory and applications of probabilistic metric spaces (I).Applied Mathematics and Mechanics (English Ed.),9, 2 (1988), 123–133.
Zhang Shisheng, Basic theory and applications of probabilistic metric spaces (II).Applied Mathematics and Mechanics (English Ed.),9, 3 (1988), 213–225.
Xiao Jianzhong. Probabilistic norm of linear operators on M-PN space and description of their boundedness,Journal of Mathematical Research and Exposition,13, 4 (1993). 631–632.
Lin Xi. Linear operators on probabilistic normed linear space.Journal of Engineering Mathematics,4, 2 (1987), 43–48.
Su Yongfu. The Hahn-Banach theorem for a class of linear functional on PN spaces and application.Journal of Inner Mongolia Teachers University (Natural Science Edition). 2 (1990), 16–17. (in Chinese)
Wang Yuankui and Mi Xianwei. Probabilistic norm of λ0 linear operators on Menger-PN space,Journal of Hebei Normal University. (Natural Science Edition), 4 (1991), 1–2. (in Chinese)
Gong Huaiyun, Linear operators on probabilistic normed spaces.Journal of Mathematical Research and Exposition,10, 2 (1990), 239–242.
Author information
Authors and Affiliations
Additional information
Communicated by Ding Xieping
Rights and permissions
About this article
Cite this article
Jianzhong, X., Xingguo, J. Probabilistic norm of linear operators on PN space. Appl Math Mech 18, 307–313 (1997). https://doi.org/10.1007/BF02453374
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02453374